Yes
No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:x = 3 if and only if x2 = 9.From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):The Conditional Statement: If x = 3 then x2 = 9.This statement is true. However, the second statement we can extract is called the converse.The Converse: If x2=9 then x = 3.This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.All it takes to prove that a statement is false is one counterexample.
false
Definition
This is not always true.
Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.
The conjunction of a conditional statement and its converse is known as a biconditional statement. It states that the original statement and its converse are both true.
No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:x = 3 if and only if x2 = 9.From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):The Conditional Statement: If x = 3 then x2 = 9.This statement is true. However, the second statement we can extract is called the converse.The Converse: If x2=9 then x = 3.This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.All it takes to prove that a statement is false is one counterexample.
No.
always true
always true
a condtional statement may be true or false but only in one direction a biconditional statement is true in both directions
An integer n is odd if and only if n^2 is odd.
No. Consider the statement "If I'm alive, then I'm not dead." That statement is true. The converse is "If I'm not dead, then I'm alive.", which is also true.
false
Definition
This is not always true.
No, the converse of a statement does not necessarily have to be true. In this case, the original statement "If you are hungry then you are not happy" does not imply that its converse "If you are not happy then you must be hungry" is always true. It is possible to be unhappy for reasons other than hunger.